Distribution of mesoscale elastic properties and mass density in the human femoral shaft

Associations between femoral 3D curvature and sagittal imbalance of spine

Background

The sagittal imbalance (SI) of spine triggers compensatory mechanisms (CMs) of lower extremity (LE) to restore trunk balance. These CMs can cause long-period stress on the femur and may possibly alter the femoral morphology. This cross-sectional observational study aimed to answer the following questions: (a) Do SI subjects exhibit greater femoral bowing compared to subjects with sagittal balance? (b) Are there associations between femoral bowing and CMs of LE in SI subjects?

Methods

Subjects who underwent biplanar full body radiographs with the EOS imaging system between January 2016 and September 2021 were recruited. Sagittal parameters included T1-pelvic angle (TPA), pelvic incidence (PI), pelvic tilt (PT), sacral slope, lumbar lordosis (LL), PI-LL, and PT/PI ratio. LE parameters were femoral obliquity angle (FOA), knee flexion angle (KA), and ankle dorsiflexion angle. Femoral bowing was quantified as 3D radius of femoral curvature (RFC). Associations between 3D RFC and the radiographic parameters were analyzed.

Results

A total of 105 subjects were included, classified into balance group (TPA < 14°, n = 40), SI group (TPA ≥ 14° and KA <5°, n = 30), and SI with knee flexion group (TPA ≥ 14° and KA ≥ 5°, n = 35). 3D RFC was significantly lower in SI with knee flexion group compared to the other two groups (both p < 0.001). Stepwise linear regression showed that age, SI and knee flexion, femoral length (FL), FOA, and KA were independent predictors for 3D RFC.

Conclusion

Greater femoral bowing is observed in subjects with SI and knee flexion compared to the balanced population. CM parameters, including KA and FOA, are associated with 3D RFC. Further longitudinal study is needed to investigate the cause-and-effect relationship between SI, CMs of LE, and femoral bowing.

Quantitative Sound Speed Imaging of Cortical Bone and Soft Tissue: Results From Observational Data Sets

This work presents the first quantitative ultrasonic sound speed images of ex vivo limb cross-sections containing both soft tissue and bone using Full Waveform Inversion (FWI) with level set (LS) and travel time regularization. The estimated bulk sound speed of bone and soft tissue are within 10% and 1%, respectively, of ground truth estimates. The sound speed imagery shows muscle, connective tissue and bone features. Typically, ultrasound tomography (UST) using FWI is applied to imaging breast tissue properties (e.g. sound speed and density) that correlate with cancer. With further development, UST systems have the potential to deliver volumetric operator independent tissue property images of limbs with non-ionizing and portable hardware platforms. This work addresses the algorithmic challenges of imaging the sound speed of bone and soft tissue by combining FWI with LS regularization and travel time methods to recover soft tissue and bone sound speed with improved accuracy and reduced soft tissue artifacts when compared to conventional FWI. The value of leveraging LS and travel time methods is realized by evidence of improved bone geometry estimates as well as promising convergence properties and reduced risk of final model errors due to un-modeled shear wave propagation. Ex vivo bulk measurements of sound speed and MRI cross-sections validates the final inversion results.

Micromechanical evaluation of cortical bone using in situ XCT indentation and digital volume correlation

The overall mechanical behaviour of cortical bone is strongly dependant on its microstructure. X-ray computed tomography (XCT) has been widely used to identify the microstructural morphology of cortical tissue (i.e. pore network, Haversian and Volkmann's canals). However, the connection between microstructure and mechanics of cortical bone during plastic deformation is unclear. Hence, the purpose of this study is to provide an in-depth evaluation of the interplay of plastic strain building up in relation to changes in the canal network for cortical bone tissue. In situ step-wise XCT indentation was used to introduce a localised load on the surface of the tissue and digital volume correlation (DVC) was employed to assess the three-dimensional (3D) full-field plastic strain distribution in proximity of the indent. It was observed that regions adjacent to the imprint were under tensile strain, whereas the volume underneath experienced compressive strain. Canal loss and disruption was detected in regions of higher compressive strains exceeding -20000 με and crack formation occurred in specimens where Haversian canals were running parallel to the indentation tip. The results of this study outline the relationship between the micromechanical and structural behaviour of cortical bone during plastic deformation, providing information on cortical tissue fracture pathways.

Age-related dynamic deformation of the femoral shaft and associated osteoporotic factors: a retrospective study in Chinese adults

Dynamic skeletal deformation with ageing showed important signs of degenerative and osteoporotic diseases. We found that both femoral bowing and cortical thickness were correlated with ageing in a Chinese population. Further, femoral cortical index, an osteoporotic indicator, was negatively correlated with femoral bowing angle. Hence, more attention should be paid to these femoral morphological changes to avoid fragility fractures and failed internal fixation.

PURPOSE

The purpose of this study was to determine whether morphological parameters of the femoral shaft are in age-related deformation and identify correlations between parameters of femoral cortical thickness and femoral shaft bowing.

METHODS

One hundred twenty patients (mean 50 years, range 18~104 years) who had received standard long-standing anteroposterior and femoral lateral radiographs from October 2016 to October 2019 were included in this retrospective study. The sagittal femoral bowing angle (sFBA), sagittal femoral cortical index (sFCI), coronal femoral bowing angle (cFBA), and coronal femoral cortical index (cFCI) were measured by two orthopaedists separately. All the participants' demographic data, including age, sex, body laterality, height, and weight, were collected. The Student's t test, Mann-Whitney U test, two-way ANOVA, Pearson correlation, and multiple linear regression were used in the statistical analysis.

RESULTS

The mean age of the male and female participants was 46.95 ± 15.25 and 52.22 ± 15.61 years, respectively. Two-way ANOVA revealed that females had a significantly lower sFCI than males at the right side (P < 0.05). There were no significant interactions between sex or body laterality and the sFBA, cFBA, sFCI, and cFCI groups (P > 0.05). Pearson correlation revealed that sFCI was strongly correlated with sFBA (r = - 0.535, P < 0.05) and cFBA (r = - 0.535, P < 0.05). Multiple linear regression analysis demonstrated that both age (β = 0.304 and 0.308 respectively) and sFCI (β = - 0.322 and - 0.414 respectively) were two independent predictors associated with sFBA and cFBA respectively.

CONCLUSIONS

The femoral shaft bowing of the Chinese population was positively correlated with ageing, whereas the sagittal femoral cortical thickness negatively correlated with ageing. A high FBA occurred in femoral shafts with a low sFCI, which revealed that femoral shaft bowing was associated with femoral cortical thickness. During femur-related surgery in older patients, more attention should be paid to these femoral morphological changes.

Estimation of Thickness and Speed of Sound in Cortical Bone Using Multifocus Pulse-Echo Ultrasound

Most bone loss during the development of osteoporosis occurs in cortical bone at the peripheral skeleton. Decreased cortical thickness (Ct.Th) and the prevalence of large pores at the tibia are associated with reduced bone strength at the hip. Ct.Th and cortical sound velocity, i.e., a surrogate marker for changes of cortical porosity (Ct.Po), are key biomarkers for the identification of patients at high fracture risk. In this study, we have developed a method using a conventional ultrasound array transducer to determine thickness (Ct.Th) and the compressional sound velocity propagating in the radial bone direction (Ct. ν₁₁ ) using a refraction-corrected multifocus imaging approach. The method was validated in-silico on porous bone plate models using a 2-D finite-difference time-domain method and ex vivo on plate-shaped plastic reference materials and on plate-shaped cortical bovine tibia samples. Plane-wave pulse-echo measurements provided reference values to assess precision and accuracy of our method. In-silico results revealed the necessity to account for inclination-dependent transmission losses at the bone surface. Moreover, the dependence of Ct. ν₁₁ on both porosity and pore density was observed. Ct.Th and Ct. ν₁₁ obtained ex vivo showed a high correlation ) with reference values. The ex-vivo accuracy and precision for Ct. ν₁₁ were 29.9 m/s and 0.94%, respectively, and those for Ct.Th were 0.04 mm and 1.09%, respectively. In conclusion, this numerical and experimental study demonstrates an accurate and precise estimation of Ct.Th and Ct. ν₁₁ . The developed multifocus technique may have high clinical potential to improve fracture risk prediction using noninvasive and nonionizing conventional ultrasound technology with image guidance.

Anisotropic elastic properties of human femoral cortical bone and relationships with composition and microstructure in elderly

The strong dependence between cortical bone elasticity at the millimetre-scale (mesoscale) and cortical porosity has been evidenced by previous studies. However, bone is an anisotropic composite material made by mineral, proteins and water assembled in a hierarchical structure. Whether the variations of structural and compositional properties of bone affect the different elastic coefficients at the mesoscale is not clear. Aiming to understand the relationships between bone elastic properties and compositions and microstructure, we applied state-of-the-art experimental modalities to assess these aspects of bone characteristics. All elastic coefficients (stiffness tensor of the transverse isotropic bone material), structure of the vascular pore network, collagen and mineral properties were measured in 52 specimens from the femoral diaphysis of 26 elderly donors. Statistical analyses and micromechanical modeling showed that vascular pore volume fraction and the degree of mineralization of bone are the most important determinants of cortical bone anisotropic mesoscopic elasticity. Though significant correlations were observed between collagen properties and elasticity, their effects in bone mesoscopic elasticity were minor in our data. This work also provides a unique set of data exhibiting a range of variations of compositional and microstructural cortical bone properties in the elderly and gives strong experimental evidence and basis for further development of biomechanical models for human cortical bone. STATEMENT OF SIGNIFICANCE: This study reports the relationships between microstructure, composition and the mesoscale anisotropic elastic properties of human femoral cortical bone in elderly. For the first time, we provide data covering the complete anisotropic elastic tensor, the microstructure of cortical vascular porosity, mineral and collagen characteristics obtained from the same or adjacent samples in each donor. The results revealed that cortical vascular porosity and degree of mineralization of bone are the most important determinants of bone anisotropic stiffness at the mesoscale. The presented data gives strong experimental evidence and basis for further development of biomechanical models for human cortical bone.

Autoregressive Signal Processing Applied to High-Frequency Acoustic Microscopy of Soft Tissues

Quantitative acoustic microscopy (QAM) at frequencies exceeding 100 MHz has become an established imaging tool to depict acoustical and mechanical properties of soft biological tissues at microscopic resolutions. In this study, we investigate a novel autoregressive (AR) model to improve signal processing and parameter estimation and to test its applicability to QAM. The performance of the AR model for estimating acoustical parameters of soft tissues (i.e., acoustic impedance, speed of sound, and attenuation) was compared to the performance of the Hozumi model using simulated ultrasonic QAM signals and using experimentally measured signals from thin (i.e., 12 and ) sections of human lymph-node and pig-cornea tissue specimens. Results showed that the AR and Hozumi methods performed equally well (i.e., produced an estimation error of 0) in signals with low, linear attenuation in the tissue and high impedance contrast between the tissue and the coupling medium. However, the AR model outperformed the Hozumi model in estimation accuracy and stability (i.e., parameter error variation and number of outliers) in cases of 1) thin tissue-sample thickness and high tissue-sample speed of sound, 2) small impedance contrast between the tissue sample and the coupling medium, 3) high attenuation in the tissue sample, and 4) nonlinear attenuation in the tissue sample. Furthermore, the AR model allows estimating the exponent of nonlinear attenuation. The results of this study suggest that the AR model approach can improve current QAM by providing more reliable, quantitative, tissue-property estimates and also provides additional values of parameters related to nonlinear attenuation.

Quantification of stiffness measurement errors in resonant ultrasound spectroscopy of human cortical bone

Resonant ultrasound spectroscopy (RUS) is the state-of-the-art method used to investigate the elastic properties of anisotropic solids. Recently, RUS was applied to measure human cortical bone, an anisotropic material with low Q-factor (20), which is challenging due to the difficulty in retrieving resonant frequencies. Determining the precision of the estimated stiffness constants is not straightforward because RUS is an indirect method involving minimizing the distance between measured and calculated resonant frequencies using a model. This work was motivated by the need to quantify the errors on stiffness constants due to different error sources in RUS, including uncertainties on the resonant frequencies and specimen dimensions and imperfect rectangular parallelepiped (RP) specimen geometry. The errors were first investigated using Monte Carlo simulations with typical uncertainty values of experimentally measured resonant frequencies and dimensions assuming a perfect RP geometry. Second, the exact specimen geometry of a set of bone specimens were recorded by synchrotron radiation micro-computed tomography. Then, a "virtual" RUS experiment is proposed to quantify the errors induced by imperfect geometry. Results show that for a bone specimen of ∼1° perpendicularity and parallelism errors, an accuracy of a few percent ( <6.2%) for all the stiffness constants and engineering moduli is achievable.